Year 8 Angles in Polygons Worksheet — Level 2 — Answers
Answer sheet with worked solutions for the Year 8 angles worksheet.
Success TutoringWorksheetsAnswer sheetYear 8 · Mathematics · AnglesYear 8 Angles in Polygons Worksheet — Level 2 — Answers
Interior angle sum = (n − 2) × 180°. The exterior angles of any convex polygon add to 360°.
1.Find the sum of the interior angles of a 14-sided polygon.
Answer: 2,160°
- Angle sum = (n − 2) × 180°
- (14 − 2) × 180° = 2,160°
2.Find the size of each interior angle of a regular decagon.
Answer: 144°
- Angle sum = (10 − 2) × 180° = 1,440°
- 1,440° ÷ 10 = 144°
3.Find the size of each exterior angle of a regular decagon.
Answer: 36°
- Exterior angles add to 360°
- 360° ÷ 10 = 36°
4.Each exterior angle of a regular polygon is 45°. How many sides does it have?
Answer: 8
- Exterior angles add to 360°
- 360 ÷ 45 = 8 sides
5.Find the sum of the interior angles of a 20-sided polygon.
Answer: 3,240°
- Angle sum = (n − 2) × 180°
- (20 − 2) × 180° = 3,240°
6.Find the size of each interior angle of a regular 18-sided polygon.
Answer: 160°
- Angle sum = (18 − 2) × 180° = 2,880°
- 2,880° ÷ 18 = 160°
7.Find the size of each exterior angle of a regular quadrilateral.
Answer: 90°
- Exterior angles add to 360°
- 360° ÷ 4 = 90°
8.Each exterior angle of a regular polygon is 72°. How many sides does it have?
Answer: 5
- Exterior angles add to 360°
- 360 ÷ 72 = 5 sides
9.Find the sum of the interior angles of a heptagon.
Answer: 900°
- Angle sum = (n − 2) × 180°
- (7 − 2) × 180° = 900°
10.Find the size of each interior angle of a regular 24-sided polygon.
Answer: 165°
- Angle sum = (24 − 2) × 180° = 3,960°
- 3,960° ÷ 24 = 165°
Marking tips
- Give credit for correct method even when the final answer slips — the working shows where the thinking went right.
- For open-ended tasks, use the success criteria as a checklist rather than looking for one "right" answer.
- Celebrate what went well first, then pick one thing to work on next.
Great work. Here's what to try next: